Article ID Journal Published Year Pages File Type
1897580 Physica D: Nonlinear Phenomena 2009 11 Pages PDF
Abstract

We propose a parametric approach to solve self-consistency equations that naturally arise in many-body systems described by nonlinear Fokker–Planck equations in general and nonlinear Vlasov–Fokker–Planck equations of Haissinski type in particular. We demonstrate for the Hess–Doi–Edwards model and the McMillan model of nematic and smectic liquid crystals that the parametric approach can be used to compute bifurcation diagrams and critical order parameters for systems exhibiting one or more than one order parameters. In addition, we show that in the context of the parametric approach solutions of the Haissinski model can be studied from the perspective of a pseudo order parameter.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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